Some new binomial sums related to the Catalan triangle

被引：0

作者：

Sun, Yidong ^{[1
]}

Ma, Fei ^{[1
]}

机构：

[1] Dalin Maritime Univ, Dept Math, Dalian 116026, Peoples R China

来源：

ELECTRONIC JOURNAL OF COMBINATORICS | 2014年 / 21卷 / 01期

关键词：

Catalan number; ballot number; Catalan triangle; PROPER RIORDAN ARRAYS; GENERATING TREES; BALLOT NUMBERS; RENEWAL ARRAYS; IDENTITIES; ENUMERATION; PATTERNS; PATHS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we derive many new identities on the classical Catalan triangle C = (C-n,C-k)(n >= k >= 0), where [GRAPHICS] are the well-known ballot numbers. The first three types are based on the determinant and the fourth is relied on the permanent of a square matrix. It not only produces many known and new identities involving Catalan numbers, but also provides a new viewpoint on combinatorial triangles.

引用

页数：15

共 50 条

[1] Factors of binomial sums from the Catalan triangle
Guo, Victor J. W.
Zeng, Jiang
JOURNAL OF NUMBER THEORY, 2010, 130 (01) : 172 - 186
[2] Catalan triangle numbers and binomial coefficients
Lee, Kyu-Hwan
Oh, Se-jin
REPRESENTATIONS OF LIE ALGEBRAS, QUANTUM GROUPS AND RELATED TOPICS, 2018, 713 : 165 - 185
[3] BINOMIAL SUMS INVOLVING CATALAN NUMBERS
Chu, Wenchang
Kilic, Emrah
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2021, 51 (04) : 1221 - 1225
[4] Sums of powers of Catalan triangle numbers
Miana, Pedro J.
Ohtsuka, Hideyuki
Romero, Natalia
DISCRETE MATHEMATICS, 2017, 340 (10) : 2388 - 2397
[5] TRIPLE PRODUCT SUMS OF CATALAN TRIANGLE NUMBERS
Chu, Wenchang
CONTRIBUTIONS TO DISCRETE MATHEMATICS, 2020, 15 (02) : 1 - 17
[6] SOME BINOMIAL SUMS
CARLITZ, L
FIBONACCI QUARTERLY, 1976, 14 (03): : 249 - 253
[7] Some Generalized Fibonomial Sums related with the Gaussian q-Binomial sums
Kilic, Emrah
Akkus, Ilker
Ohtsuka, Hideyuki
BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE, 2012, 55 (01): : 51 - 61
[8] Exponential sums with Catalan numbers and middle binomial coefficients
Garaev, Moubariz Z.
Luca, Florian
Shparlinski, Igor E.
INDAGATIONES MATHEMATICAE-NEW SERIES, 2007, 18 (01): : 23 - 37
[9] Divisibility of some binomial sums
Ni, He-Xia
Pan, Hao
ACTA ARITHMETICA, 2020, 194 (04) : 367 - 381
[10] Some binomial identities related to the Catalan triangles and the halves of the Pascal matrix
Yang, Lin
Yang, Sheng-Liang
FILOMAT, 2023, 37 (20) : 6917 - 6924

← 1 2 3 4 5 →